The correct answer is: "fear that joining the League of Nations meant the US was obligated to get involved with future European conflicts".
After its participation in WWI, the US adopted a isolationist approach with regard to foreign policy issues. The US government decided not to maintain previous alliances in order to focus better on domestic issues, rather than on external affairs.
The League of Nations was created in 1920, after WWI, to promote cooperation among previously confronted countries in order to prevent future warfare and ensure world peace. The US government believed that participating in the LN would, up to a point, obly them to side with one party in case of a conflict, and this was not compatible with their isolationist desires.